Optical sensing with tessellated diffraction-pattern generators

ABSTRACT

An array of diffraction-pattern generators employ phase anti-symmetric gratings to projects near-field spatial modulations onto a closely spaced array of photoelements. Each generator in the array of generators produces point-spread functions with spatial frequencies and orientations of interest. The generators are arranged in an irregular mosaic with little or no short-range repetition. Diverse generators are shaped and placed with some irregularity to reduce or eliminate spatially periodic replication of ambiguities to facilitate imaging of nearby scenes.

BACKGROUND

A planar Fourier capture array (PFCA) is an image sensor that does notrequire a lens, mirror, or moving parts. As a consequence, cameras thatemploy PFCAs to acquire image data can be made extraordinarily small andinexpensive. PFCAs include angle-sensitive pixels whose sensitivity tolight is a sinusoidal function of incident angle within the imager'sfield of view. The measurement from one photodiode from a PFCA can beinterpreted as a measure of one component of the two-dimensional (2D)Fourier transform of a far-away scene. Each pixel has physicalcharacteristics that make is sensitive to a distinct component of the 2DFourier transform of the far-away scene. Taken together, thesecomponents relate full Fourier information representative of the scene.Some applications may use the Fourier components directly, or images ofthe scene can be computationally reconstructed.

PFCAs exploit a near-field diffraction effect named for Henry Fox Talbot(the “Talbot effect”). Briefly, a plane wave incident upon a periodicdiffraction grating produces a repeating image of the grating at regulardistances away from the grating plane. A second grating, or “analyzer,”beneath the first grating passes or blocks the image depending on theincident angle. The resultant pattern is then captured by a conventionalphotodetector array. Finally, the subject of the image is resolvedcomputationally from the captured pattern.

The spacing between the grating layers, and between the grating layersand the photodetector array, can be very difficult to manufacture withsufficient precision to ensure that the analyzer layer and thephotodetector array fall precisely at the regular distances thataccurately reproduce a Talbot image. In standard CMOS processes, forexample, interlayer thicknesses can vary by 20%. Also problematic,Talbot spacing is a strong function of wavelength, making it exceedinglydifficult to produce sharp Talbot images over some wavelength bands ofinterest (e.g., the visible light spectrum).

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description is illustrated by way of example, and not byway of limitation, in the figures of the accompanying drawings and inwhich like reference numerals refer to similar elements and in which:

FIG. 1A is a cut-away view of an imaging device 100 with a phaseanti-symmetric grating 105 overlying a photodetector array 110;

FIG. 1B depicts sensor 100 of FIG. 1A simulating light incident plane120 at an acute angle 160 to illustrate the sensitivity of curtains 140and foci 145 to the angle of incidence.

FIG. 2 depicts a one-dimensional, binary phase anti-symmetric grating200 in accordance with one embodiment.

FIG. 3A depicts an imaging device 300 in accordance with an embodimentin which a binary, phase anti-symmetric grating 310 is formed by aninterface between light-transmissive media of different refractiveindices.

FIG. 3B depicts an imaging device 350 similar to device 300 of FIG. 3A,but equipped with an array of microlenses 365 disposed over thephotoelements.

FIG. 4 is a cut-away view of an imaging device 400 with a phaseanti-symmetric grating 405 overlying a photodetector array 410 andilluminated by a pair of nearby point sources 415 and 420.

FIG. 5 is a cut-away view of an imaging device 500 with a phaseanti-symmetric grating 505 with disparately spaced odd-symmetryboundaries.

FIG. 6 is a cut-away view of an imaging device 600 in accordance withanother embodiment.

FIG. 7 depicts a flow cytometer 700 in accordance with one embodiment,and is here used to illustrate the challenge of imaging in twodimensions for a very near scene.

FIG. 8A is a plan view of a sensor 800 in accordance with anotherembodiment.

FIG. 8B is a side view of sensor 800 of FIG. 8A with a blood cell 820 inclose proximity to illustrate a problem with imaging nearby objects.

FIG. 8C is a side view of a sensor 830 of FIG. 8B in accordance with anembodiment that improves near-field imaging.

FIG. 8D is a three-dimensional perspective of a sensor 830 of FIG. 8C.

FIG. 9 is a plan view of a sensor 900 in accordance with an embodimentin which identical gratings 905 are arrayed e.g. for improved sensing ofnearby objects.

FIG. 10A is a plan view of a grating 1000 in accordance with anotherembodiment.

FIG. 10B depicts the shapes of boundaries 1005 of FIG. 10A.

FIG. 11A depicts a sensor 1100 that includes tessellateddiffraction-pattern generators 1105 overlying a regular array ofphotoelements 1110.

FIG. 11B is a plan view of sensor 1100 of FIG. 11A that more clearlyshows the diversity of generators 1105.

FIG. 12 depicts a number of alternative patterns of tessellateddiffraction-pattern generators.

FIG. 13 depicts a number of alternative patterns of tessellateddiffraction-pattern generators.

FIG. 14A depicts a sensor 1400 in accordance with another embodiment.

FIG. 14B depicts 16 per-pixel analyzer patterns used in FIG. 14A tocreate the pattern of analyzer 1405.

FIG. 15A depicts an infrared sensor 1500 in accordance with anembodiment in which a binary, phase anti-symmetric grating 1510 of ahigh-density polyethylene (HDPE) is separated from an array ofphotoelements 1520 by an air interface 1525.

FIG. 15B is a plan view of grating 1510 in accordance with an embodimentfor IR imaging as in FIG. 15A.

FIG. 16 shows a portion of a grating 1600, showing relatively thin andthick areas 1605 and 1610, in accordance with another embodiment.

DETAILED DESCRIPTION

FIG. 1A is a cut-away view of an imaging device 100 with a phaseanti-symmetric grating 105 overlying a photodetector array 110, such asa CCD (charge-coupled device), CMOS (complementarymetal-oxide-semiconductor) or (in the case of midwave IR detection) amicrobolometer sensor. The photodetector array may comprise a lensletarray designed to concentrate incident photons onto the most sensitiveareas of the array to increase quantum efficiency. The features ofgrating 105 offer considerable insensitivity to the wavelength ofincident light in a wavelength band of interest, and also to themanufactured distance between grating 105 and photodetector array 110.Grating 105 produces an interference pattern for capture by array 110.Digital photographs and other image information can then be extractedfrom the pattern.

Light in a wavelength band of interest is striking grating 105 from adirection 115 that is normal to a transverse plane 120 of the grating105. Unless otherwise stated, the wavelength band of interest is thevisible spectrum. Cameras developed for use in different applicationscan have different bands of interest, as is well understood by those ofskill in the art.

Dashed lines 125 highlight periodic boundaries between regions of phaseanti-symmetry. Each of these boundaries is a result of features 130 and135 of odd symmetry, and produces a normally arranged curtain 140 ofminimum intensity created by destructive phase interference betweenadjacent features 130 and 135. Curtains 140 are separated by foci 145(curtains of maximum light intensity), and the collection of curtains140 and foci 145 extend from grating 105 through the body 150 of device100 to produce an interference pattern on photodetector array 110. Inthis illustration, the pattern of intensity variations evident in thefoci and curtains are near-field spatial modulations that result fromnear-field diffraction. One photosensitive element 155 within array 110is shaded beneath a focus 145 to serve as a reference for a subsequentdiscussion of the sensitivity of device 100 to the angle of incidentlight.

The image of FIG. 1A resulted from a simulation of an imaging devicewith the following parameters and assuming specific parameters. Body 150is of fused silica, and is in contact with a conventional photodetectorarray 110 with photosensitive elements spaced by 2.2 μm. The top ofgrating 105 is an air interface in this example. The relatively smallsegments of features 130 and 135 are about and the relatively largersegments are about 4 μm. These segments generally form transverse plane120, which is separated from array 110 by about 25 μm. Curtains 140 andfoci 145 are the destructive and constructive interference patterns for532 nm incident light.

The thickness of body 150 and lengths of the segments of features 130and 135 were optimized for 400 nm light despite the selection of 532 nmlight for the simulation. As a consequence, the tightest focus occursabout 5 μm above array 110 (at the 20 μm mark). The resultant curtains140 plainly separate foci 145 well above and below the 20 μm mark,however, illustrating a robust insensitivity to wavelength within theband of interest. The relatively deep and continuous penetration ofcurtains 140 also provides considerable manufacturing tolerance for thethickness of body 150. These advantages obtain because the near-fieldspatial modulations projected onto array 110 are wavelength independentover the wavelength band of interest, which means that the adjacentmodulations (dark and light) do not reverse signs with changes inwavelength within the band of interest.

FIG. 1B depicts imaging device 100 of FIG. 1A simulating light incidentplane 120 at an acute angle 160 to illustrate the sensitivity ofcurtains 140 and foci 145 to the angle of incidence. Using element 155as a reference point, we see that that the foci 145 that illuminatedelement 155 in FIG. 1A have considerably moved to the right in FIG. 1B.Curtains 140 and foci 145 extend at an acute angle that relates to angle160 according to Snell's law. The separation of foci 145 by curtains 140is maintained. Imaging device 100 is thus sensitive to the angle ofincidence.

Each phase anti-symmetric structure generates a diffraction pattern, andthe resultant collection of patterns is itself a pattern. For a pointsource, this pattern of light intensity on the sensor is called a“point-spread function” (PSF). As used herein, a “diffraction-patterngenerator” is a structure that produces PSFs for light within thewavelength band of interest, and for a range of orientations ofinterest. In this one-dimensional example, the orientation of interestis perpendicular to the boundaries of odd symmetry.

FIG. 2 depicts a one-dimensional, binary phase anti-symmetric grating200 in accordance with one embodiment. The upper features of grating 200are at a height Xλ(2(n−1)), sufficient to induce one-half wavelength ofretardation in the band of interest relative to lower features, or πradians of relative phase delay. Features 205 and 210 on either side ofeach boundary exhibit odd symmetry with three differently sized segmentsW₀, W₁, and W₂. With this arrangement, paired segments (e.g., W₀ withinfeatures 205 and 210) induce respective phase delays that differ byapproximately half a wavelength over the wavelength band of interest.

FIG. 3A depicts a imaging device 300 in accordance with an embodiment inwhich a binary, phase anti-symmetric grating 310 is formed by aninterface between light-transmissive media of different refractiveindices, a polycarbonate layer 315 and optical Lanthanum dense flintglass 320 in this example. Each of four boundaries of odd symmetry 325is indicated using a vertical, dashed line. As in the foregoingexamples, the upper features of grating 310 induce phase retardations ofhalf of one wavelength (it radians) relative to lower features. Features330 and 335 on either side of each boundary exhibit odd symmetry. Withthis arrangement, paired features induce respective phase delays thatdiffer by approximately half a wavelength over the wavelength band ofinterest.

Due to dispersion, the difference in the refractive index ofpolycarbonate layer 315 and Lanthanum dense flint glass layer 320 is anincreasing function of wavelength, facilitating a wider wavelength bandof interest over which the phase delay is approximately π radians. Theseelements produce an interference pattern on an analyzer layer 327 (e.g.,a conventional photodiode array) in the manner detailed in connectionwith FIGS. 1A and 1B.

This example assumes light incident the light interface of grating 310is normal to the transverse plane of phase grating 310, in which caselight fields that enter grating 310 equidistant from a one of theboundaries of odd symmetry 325, such as at locations (−X,0) and (X,0),are out of phase at points beneath array 310 (e.g., point (0,Z)), andthus destructively interfere to produce curtains of minimum intensity(e.g., curtains 140 of FIG. 1). Neither the depth Z nor the wavelengthof light over a substantial spectrum significantly influences thisdestructive interference. Constructive interference similarly producesfoci of maximum intensity (e.g., foci 145 of FIG. 1). Both the high andlow features admit light, which provides relatively high quantumefficiency relative to gratings that selectively block light.

The following discussion details phase gratings in accordance withexamples described in P. R. Gill and D. G. Stork, “LenslessUltra-Miniature Imagers Using Odd-Symmetry Spiral Phase Gratings,” inImaging and Applied Optics, J. Christou and D. Miller, eds., OSATechnical Digest (online) (Optical Society of America, 2013). In thatarticle, Gill and Stork describe a phase grating formed by a high-n,low-dispersion substrate and a low-n, high-dispersion coating that canintroduce approximately λ-independent phase shifts in all normallyincident visible light. Similar gratings are discussed above. If thereexist certain points p on this interface that satisfy the followingsymmetry in their transmission t (•) and phase retardation φ(•),

t(p+y)=t(p−y)∀y   (1)

φ(p+y)=φ(p−y)+π+2nπ∀y, n∈{0, ±1, ±2, . . . }  (2)

where y is a horizontal translation transverse to the grating direction,then the grating has phase anti-symmetry about points p, and light willinterfere destructively below p, regardless of λ and depth z.

A linear phase anti-symmetric grating above a photosensor array couldpass information from a single spatial orientation of features in thefar field (transverse to the grating orientation). However, to captureinformation about arbitrarily oriented features of a complex scene, itis preferable to have a complete distribution of orientations in thediffractive optic. More generally, if the point-source responses (PSRs)are approximately spatially invariant, the transfer function of theimager approximates convolution with the PSR function. In such a case,the PSR should have significant power at all 2D spatial frequencies tomake the inversion problem of image recovery well-conditioned.

In one example provided in Gill and Stork, gratings were numericallyoptimized to focus visible light onto a photodetector array 100 μmbelow. Optical simulations estimated the imaging performance of such adevice from a 60×60 pixel array with 2.2 μm pitch 100 μm below thegratings with the sensor illuminated by a complex scene far (

100 μm) from the sensor. The resultant photocurrent from the pixel arraywas unintelligible when digitized and viewed directly as a digitalimage; however, the scene was reconstructed to a higher resolution thanpossible using a much larger PFCA using Tikhonov regularization. Gilland Stork report that compressed sensing techniques could be applied toimprove the reconstruction quality if the scene is known to have acompressible structure. Compressed sensing could be especiallyadvantageous if small gaps in the Fourier transform of the PSR exist.

FIG. 3B depicts an imaging device 350 similar to device 300 of FIG. 3A,with like-identified elements being the same or similar. In thisembodiment the light-transmissive media between grating 310 and analyzerlayer 327 includes a flint glass layer 355 and an air interface 360. Anarray of microlenses 365 disposed over analyzer layer 327 focuses lightonto the photoelements, each being coincident with a single photoelementin this example.

Near-Object Imaging

Phase anti-symmetric gratings of the type detailed herein supportlensless cameras with considerably greater depths of field than moreconventional imaging devices. Resolving very near objects still presentsa challenge, however. Applications for near-field cameras include paperhandling, flow cytometry, defect inspection, web inspection, andfingerprint scanning.

FIG. 4 is a cut-away view of an imaging device 400 with a phaseanti-symmetric grating 405 overlying a photodetector array 410 andilluminated by a pair of nearby point sources 415 and 420. Odd-symmetryboundaries are evenly spaced by a distance S. Dashed lines from sources415 and 420 respectively represent diverging wavefronts for lightincident grating 405. The portions of those lines withinlight-transmissive medium 425 can be said to represent the “curtains” ofodd symmetry introduced previously. Sources 415 and 420 are very near tograting 405. As one measure of “near,” sources are within a distance ofS²/λ, where S is the spacing introduced in FIG. 4. Imaging devices inaccordance with some embodiments can image objects over a depth of fieldfrom S²/λ to infinity. Other near-object embodiments may not workoptimally at infinity.

Due to the relative proximity of the imaged point sources 415 and 420,light incident array 410 enters medium 425 over a considerable range ofangles. Light entering medium 425 via different diffraction-patterngenerators can produce curtains that impinge upon the same photoelement,leading to some ambiguity. In this example, three curtains from pointsource 415 produce intensity minima at the same three photosensors 435as do curtains from point source 420. The resultant ambiguity makes itdifficult to distinguish between point sources 415 and 420.

FIG. 5 is a cut-away view of an imaging device 500 with a phaseanti-symmetric grating 505 with disparately spaced odd-symmetryboundaries. But for the variety of spacings S1-S4, grating 505 is likethe example of FIG. 4, with like-identified elements being the same orsimilar. The disparate spacings of the diffraction-pattern generatorsproduce different patterns for the point sources that were ambiguous inthe example of FIG. 4. Unequal generator spacing can introduce ambiguityfor other point sources, but prevents spatially periodic replication ofthe same ambiguity over different regions of array 410.

FIG. 6 is a cut-away view of an imaging device 600 in accordance withanother embodiment. As in the example of FIG. 4, device 600 includes anevenly spaced, phase anti-symmetric grating 405 overlying aphotodetector array 410. Device 600 additionally includes an analyzer605, which is in this example a grating that selectively blocks incominglight. Foci between adjacent curtains are selectively blocked byanalyzer 605 to provide angle sensitivity that resolves ambiguity. Alsobeneficial, the inclusion of analyzer 605 can improve resolution. Forexample, if features produced by the generators are narrower than thepixel pitch of array 410, a suitably optimized analyzer could alias thisinformation so that photocurrent from array 410 is sensitive toless-than-single pixel shifts in the interference pattern. Both thegrating and the analyzer are regular in this example, but in otherembodiments the grating, the analyzer, or both can have a variety ofshapes and spacings.

FIG. 7 depicts a flow cytometer 700 in accordance with one embodiment,and is here used to illustrate the challenge of imaging in twodimensions for a very near scene. Flow cytometers are used for cellcounting, cell sorting, biomarker detection and protein engineering.Particles of interest are suspended in a stream of fluid and passed byan electronic detection apparatus. In this example, cytometer 700includes a channel 705, illuminated from the side, through which bloodflows over a two-dimensional image sensor 710 in accordance with oneembodiment. Light strikes the sides of blood cells 715 and is deflecteddown onto sensor 710 to appear (when properly focused) as bright spotsagainst a relatively dark background. Data from sensor 710 can beanalyzed to derive various types of information about physical andchemical attributes of blood cells 715 individually and collectively.

Cytometer 700 is ideally small and inexpensive, both characteristicscalling for a close separation between channel 705 and sensor 710. Thisarrangement leads to the same problem introduced in connection with FIG.4; namely, due to the relative proximity of the imaged cells, lightenters sensor 710 over a considerable range of angles, which leads tosome spatial ambiguity. This problem is exacerbated in two dimensionalimaging systems by the need for orientation information.

FIG. 8A is a plan view of a sensor 800 in accordance with anotherembodiment. Relatively high segments 805 and low segments 810 on eitherside of each of eight boundaries of odd symmetry 815 create a grating inwhich the boundaries diverge from the center of sensor 800 such that thewidths of the segments increase toward the periphery. For a given focaldepth, light of higher frequencies tends to produce a sharper focus withnarrower feature widths. Sensor 800 can therefore be optimized such thatthe central portion of the grating is optimized for collection ofrelatively higher frequency light, and the peripheral area forcollection of relatively lower frequency light. Boundaries 815 arestraight and continuous in this example, but may be curved,discontinuous, or both in other embodiments.

FIG. 8B is a side view of sensor 800 of FIG. 8A with a blood cell 820 inclose proximity to illustrate a problem with imaging nearby objects.Wavefronts from objects or point sources relatively near sensor 800,from a perspective normal to the depicted surface, impinge upon thesensor surface over a relatively broad range of angles. If the anglesare too extreme, light evincing some orientations cannot be imaged. Inthe depicted example, blood cell 820 is in close proximity to sensor 800and over the leftmost corner. Light from the blood cell that impingesupon sensor 800 along boundary 825 is incident at too acute an angle tobe properly resolved by sensor 800, or even to enter the surface. Thecaptured PSF would therefore lack the full complement of orientationdata for resolving blood cell 820.

FIG. 8C is a side view of a sensor 830 of FIG. 8B in accordance with anembodiment that improves near-field imaging. The generator pattern ofsensor 800 is replicated four times over the same area as in the exampleof FIG. 8B (i.e., each generator has a width W/2). The smallergenerators provide a full complement of orientation information over asmaller range of incident angles to that the captured PSF would providemore orientation data from which to resolve blood cell 820. Toillustrate this point, one ray entering sensor 830 is shown to passthrough a boundary 835 that provides the same orientation information asboundary 825 of FIG. 8B.

FIG. 8D is a three-dimensional perspective of a sensor 830 of FIG. 8C.Light 840 from a direction normal to the grating surface casts aninterference pattern on an underlying photodiode array 845. Curtains andfoci, as detailed previously, respectively cast shadows 850 and brightshapes 855 to be sensed by individual photosensitive elements of array845. Array 845 captures a digital representation of the resultingpattern. Because the grating pattern instances have considerably lessarea than in the prior example, light from a given point impinges a fullset of odd-symmetry features over a smaller range of incident angles.

FIG. 9 is a plan view of a sensor 900 in accordance with an embodimentin which identical grating pattern instances 905 are arrayed e.g. forimproved sensing of nearby objects. Assume, for example, that light froma point source directly above the upper-left grating pattern instance905 impinges upon the upper-right array at angles too acute to enter theupper-right array, and that that light from a point source directlyabove the upper-right grating pattern instance likewise cannot enter theupper-left array. Sensor 900 can nevertheless image both point sourcesbecause each grating pattern instance 905 images sufficient orientationinformation. A single larger grating pattern instance of the same areaas sensor 900 would not sense the requisite orientation information fortwo such point sources.

Each of grating pattern instances 905 is identical, but any number ofparameters can be varied within and among grating pattern instances 905.For example, different shapes and types of grating instances can be usedto create and image different types of interference patterns that can becombined or used separately to obtain some desired result, for exampleavoiding the ambiguity introduced by devices with strict orsmall-pitched periodicity. The decision to consider all or a specificsubset of information generated by one or more of the constituentgrating instances can be done once, such as at time of manufacture toaccommodate process variations, or can be done dynamically to highlightdifferent aspects of a scene. Emphasizing aspects of different patternscan be used, for example, to highlight light of different polarizations,wavelengths, or angles of incidence.

FIG. 10A is a plan view of a grating 1000 in accordance with anotherembodiment. Recalling that relatively narrow (wide) segment spacingworks better for relatively high (low) frequencies, feature spacingincreases along odd-symmetry boundaries (between elevated and recessedgrating regions, represented by dark and light) with distance from thecenter. Curved boundaries of odd symmetry 1005 extend radially from thecenter of the grating to the periphery, radiating out between the dark(elevated) and light (recessed) arms near the center. The curvedboundaries are obscured by grating features in FIG. 10A, so the shapesof boundaries 1005 are depicted in FIG. 10B for ease of review. Thesegment widths do not continue to increase with radius, as there is amaximum desired width for a given wavelength band of interest (e.g., thewidest may correspond to the lowest frequency of visible red light). Thefeatures that define boundaries 1005 therefore exhibit discontinuitiesas they extend toward the periphery of grating 1000. In this example,grating 1000 has three discrete areas each tuned to a subset or all ofthe wavelengths in the band of interest.

Grating 1000 does not tessellate efficiently, as is desirable for thereasons noted above in connection with FIG. 8A through FIG. 9. Theinventors have therefore developed area-efficient gratings that offerorientation diversity for broad ranges of spatial frequencies.

FIG. 11A depicts a sensor 1100 that includes tessellateddiffraction-pattern generators 1105 overlying a regular array ofphotoelements 1110. Each generator 1105 occupies an area (the “generatorarea”) considerably greater than the area occupied by one of theunderlying photoelements 1110 (the “element area”). In this embodimenteach photoelement is capable of resolving a location of photon arrivalto within an element area less than one sixth of the generator area. Thelight-transmissive media separating generators 1105 from photoelements1110 allows light to propagate horizontally as well as vertically, solight entering medium sensor 1100 at different angles and via differentgenerators 1105 can produce curtains that impinge upon the samephotoelement.

Sensor 1100 overcomes the angle limitations detailed above in connectionwith FIGS. 8B and 9 to effectively image nearby objects. Sensor 1100differs from sensor 900, however, in that the constituent generators1105 have spiral patterns that produce PSFs with most or all of thespatial frequencies and orientations of interest. Moreover, generators1105 are not identical, but are shaped and placed with some irregularityto reduce or eliminate spatially periodic replication of ambiguities. Asa consequence of this irregularity, adjacent generators 1105 exhibitslightly different PSFs for the spatial frequencies of interest andavoid the type of ambiguity seen by the device in FIG. 4. The ranges ofspatial frequencies sensed by adjacent generators overlap considerably,and are essentially the same in some embodiments.

FIG. 11B is a plan view of sensor 1100 of FIG. 11A that more clearlyshows the diversity of generators 1105. Each generator 1105 is unique inthis irregular mosaic, but other embodiments have similar short-rangeirregularity but exhibit a longer-range order. For example, gratings canbe arranged in rows and columns, with varied but repeated spacingbetween rows, columns, or both. Rows and columns can be distorted, as byimposing sinusoidal or other forms of curvature onto the mosaic toproduce a pattern of gratings that does not exhibit short-rangerepetition.

FIG. 12 depicts a number of alternative patterns of tessellateddiffraction-pattern generators. In each example, neighboring generatorsgive overlapping ranges of orientations and spatial frequencies, forwavelengths within the band of interest. In some examples the generatorsare arranged in regular mosaics (with evenly spaced rows and columns).In other examples the generators are varied in e.g. size, shape, andspacing to produce irregularity between neighboring generators andthereby reduce source location ambiguity.

FIG. 13 depicts a number of alternative patterns of tessellateddiffraction-pattern generators. At the upper left, a one-dimensionalgenerator pattern provides diverse spacing for but one orientation. Atthe upper right is a test pattern. The pattern at the lower leftillustrates generator diversity via spatial warping. Finally, thepattern at the lower right is a non-tessellated array of two-arm spiralsthat achieves orientation diversity using distinct rotation angles.

FIG. 14A depicts a sensor 1400 in accordance with another embodiment.Sensor 1400 is like sensor 900 of FIG. 9, with like-identified elementsbeing the same or similar. Recalling the foregoing discussion of FIG. 6,an angle-sensitive analyzer can be used in lieu of, or in addition to,an irregular array of generators to resolve ambiguity and improve imageresolution. Sensor 1400 includes an analyzer 1405, shown in plan view,between the generators and an underling sensor array (not shown).Adjacent generators are each sensitive to the same ranges of spatialfrequencies and orientations in this embodiment, but randomizedper-pixel patterns in the analyzer layer scramble the sampledinterference pattern.

FIG. 14B depicts 16 per-pixel analyzer patterns used in FIG. 14A tocreate the pattern of analyzer 1405.

FIG. 15A depicts an infrared sensor 1500 in accordance with anembodiment in which a binary, phase anti-symmetric grating 1510 of ahigh-density polyethylene (HDPE) is separated from an array ofphotoelements 1520 by an air interface 1525. Each of four boundaries ofodd symmetry 1530 is indicated using a vertical, dashed line. Theseelements produce an interference pattern on array 1520 in the mannerdetailed in connection with FIGS. 1A and 1B. Any array of lenses may beincluded, in which case each lens may be coincident with a singlephotoelement.

This example assumes light incident the light interface of grating 1510is normal to the transverse plane of phase grating 1510, in which caselight fields that enter grating 1510 equidistant from a one of theboundaries of odd symmetry 1530, such as at locations (−X,0) and (X,0),are out of phase at points beneath array 1510 (e.g., point (0,Z)), andthus destructively interfere to produce curtains of minimum intensity(e.g., curtains 140 of FIG. 1).

Phase grating 1510 is much less than one millimeter thick, and thusadmits most of the incident infrared (IR) light. The refractive index ofHDPE for 10 μm IR radiation is approximately 1.54. Thick regions 1535 ofgrating 1510 are 10 μm taller than thin regions 1540, and thus introduceapproximately a half-wavelength retardation compared to thin regions. Inthis example, grating 1510 is 50 μm thick at its thickest and 40 μmthick at its thinnest, and the separation between grating 1510 and theunderlying IR sensor 1520 (for instance, a microbolometer) is 2 mm. Theair gap between grating 1510 and array 1520 allows the grating to bethin, which advantageously limits IR absorption.

FIG. 15B is a plan view of grating 1510 in accordance with an embodimentfor IR imaging as in FIG. 15A. Grating 1510 is similar to grating 1000of FIGS. 10A and 10B, but with larger dimensions optimized for thelonger wavelength of IR light as compared with the visible spectrum. Asin the prior example, relatively narrow (wide) segment spacing worksbetter for relatively high (low) frequencies, and feature spacingincreases along odd-symmetry boundaries (between dark and light regions)with distance from the center. The microbolometer in this embodimentmeasures 2 mm by 2 mm, and the pattern on the film is a single 6-armspiral 1550. The pixel pitch of array 1520 is 33.3 μm.

FIG. 16 shows a portion of a grating 1600, showing relatively thin andthick areas 1605 and 1610, in accordance with another embodiment.Grating 1600 is e.g. molded HDPE, and includes arrays of micro-pillars1615 on the top and bottom surfaces. In one embodiment of a sensor thatemploys such a grating, each micro-pillar 1615 is 2 μm tall and 3 μmwide, and the collection of pillars covers 45% of the surfaces. Thepillar dimensions are smaller than the wavelength of IR light, so theycollectively act like a material with an intermediate refractive index.The collections of micro-pillars 1615 act as quarter-wavelengthantireflective coatings to the n=1.54 plastic HDPE film. Amicrobolometer used in this sensor can have a 33.3 micron-pitch, 240×240pixels, making it 8 mm by 8 mm. Grating 1600 is 12 mm by 12 mm, centeredover the microbolometer, and is separated from the microbolometer by 4mm. Grating 1600 has e.g. a tessellated pattern of 6-arm spirals. Forthe IR sensor in accordance with the device described in FIG. 16,individual grating features may be 41% larger than for the device ofFIG. 15 (twice the height, so the gratings are the square of root 2times as wide), and approximately 18 whole spirals fit into the 12×12 mmarea. The phase gratings can be arrayed, tessellated, and distorted asdetailed previously for other sensors.

While the subject matter has been described in connection with specificembodiments, other embodiments are also envisioned. For example; whileeach grating detailed previously may be used in connection withphotoreceptors to collect incident light, gratings in accordance withthese and other embodiments can be used more generally in imagingdevices that project images using photoelements that admit light;cameras described as using lenses could also employ other types ofoptical elements (e.g., mirrors); the wavelength band of interest can bebroader or narrower than the visible spectrum, may be wholly orpartially outside the visible spectrum, and may be discontinuous; andcameras and gratings detailed herein can be adapted for use inmulti-aperture or programmable-aperture applications. Other variationswill be evident to those of skill in the art. Therefore, the spirit andscope of the appended claims should not be limited to the foregoingdescription. Only those claims specifically reciting “means for” or“step for” should be construed in the manner required under the sixthparagraph of 35 U.S.C. §112.

What is claimed is:
 1. An imaging device comprising: adjacentdiffraction-pattern generators each occupying a generator area from aperspective normal to the generators; an array of photoelements eachcapable of resolving a location of photon arrival from the perspectivenormal to the generators; and a light-transmissive medium allowing lightincident adjacent ones of the generators to intersect the same one ofthe photoelements.
 2. The imaging device of claim 1, wherein adjacentones of the diffraction-pattern generators, responsive to the light,exhibit point-spread functions representing respective overlappingranges of spatial frequencies.
 3. The imaging device of claim 1, furthercomprising an analyzer disposed between the diffraction-patterngenerators and the array of photoelements to selectively block a portionof the light.
 4. The imaging device of claim 3, wherein the analyzercomprises programmable apertures.
 5. The imaging device of claim 1,wherein the adjacent diffraction-pattern generators are irregularlyshaped and placed.
 6. The imaging device of claim 5, wherein theadjacent diffraction-pattern generators exhibit different point-spreadfunctions.
 7. The imaging device of claim 1, wherein thediffraction-pattern generators are organized in a linear array.
 8. Animaging device comprising: adjacent diffraction-pattern generators eachoccupying a generator area from a perspective normal to the generators,the diffraction-pattern generators each including boundaries that extendover angles from the perspective normal to the generators and producenormally arranged curtains of minimum intensity; an array ofphotoelements each capable of resolving a location of photon arrivalfrom the perspective normal to the generators, wherein the normallyarranged curtains of minimum intensity extend to the array ofphotoelements; and a light-transmissive medium allowing light incidentadjacent ones of the generators to intersect the same one of thephotoelements.
 9. The imaging device of claim 8, wherein the curtains ofminimum intensity extend unbroken to the array of photoelements.
 10. Theimaging device of claim 8, wherein the boundaries separate features ofodd symmetry, each of the curtains of minimum intensity created bydestructive phase interference between first phase-generator featureslocated to one side of the curtain of minimum intensity and pairedsecond phase-generator features located to the other side of the curtainof minimum intensity.
 11. The imaging device of claim 8, furthercomprising an analyzer disposed between the diffraction-patterngenerators and the array of photoelements to selectively block a portionof the light.
 12. The imaging device of claim 11, wherein the analyzercomprises dissimilar analyzer patterns.
 13. The imaging device of claim12, wherein the adjacent diffraction-pattern generators are irregularlyshaped and placed.
 14. The imaging device of claim 11, wherein theanalyzer comprises programmable apertures.
 15. The imaging device ofclaim 8, wherein adjacent ones of the diffraction-pattern generators,responsive to the light, exhibit point-spread functions representingrespective overlapping ranges of spatial frequencies and overlappingorientations.
 16. The imaging device of claim 8, wherein thelight-transmissive medium includes an air interface.
 17. The imagingdevice of claim 8, further comprising an array of lenses coincident thearray of photoelements.
 18. The imaging device of claim 17, wherein eachlens is coincident with only one of the photoelements.
 19. The imagingdevice of claim 8, the diffraction-pattern generators comprising pillarsoccupying the generator areas.
 20. The imaging device of claim 19,wherein the pillars includes a set extending away from the photoelementsand a second set extending toward the photoelements.
 21. An imagingdevice comprising: pattern-generation means each occupying an area ofincident light, each pattern-generation means producing normallyarranged curtains of minimum intensity responsive to the incident light;an array of photoelements each capable of resolving a location of photonarrival from a perspective normal to the pattern-generation means,wherein the normally arranged curtains of minimum intensity extend tothe array of photoelements; and a light-transmissive medium allowing theincident light on adjacent ones of the pattern-generation means tointersect the same one of the photoelements.